Non-Hermitian extension of the topological phase in one-dimensional systems has recently attracted a great deal of attention. In particular, NHSE was shown to break the standard bulk-boundary correspondence principle since eigenstates that are not at the Bloch points are localized at the edge of the open lattice [1]}, [2]}. NHSE that can be predicted using the spectral winding number [3]} implies that the spectra in the complex energy plane are highly sensitive to the boundary conditions [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}. The spectra form a loop/loops under the periodic boundary conditions, and becomes topologically nontrivial. On the other hand, a topological phase transition occurs and the system become topologically trivial in terms of a point gap under open boundary conditions [33]}, [34]}, [35]}, [36]}.
